Note that ()–() are precisely the Karush-Kuhn-Tucker (KKT)
conditions (see [1]} and
[2]}) for the optimization program:
\(\max _{0\preceq \mathbf {B}\preceq \mathbf {S}}\left[\sum _{k=1}^K\frac{\mu _k}{2}\log |\mathbf {B}+\mathbf {N}_k|-\frac{1}{2}\log |\mathbf {B}+\mathbf {N}_0|\right].\) 
